You'll need your employer to sponsor you for employment-based green card - you can't self-sponsor.
However, TN visa is single-intent and meant to be temporary, i.e. you can't immigrate on this visa. This is different from dual intent visas H1B and L1 where they are dual intent.
This means that you can't travel until you are granted Advance Parole. This can mean a year or two waiting in limbo in the US.
Source: in the process for employment based green card and have a few friends who switched from TN/E3 visa to green card
However, TN visa is single-intent and meant to be temporary, i.e. you can't immigrate on this visa. This is different from dual intent visas H1B and L1 where they are dual intent.
This means that you can't travel until you are granted Advance Parole. This can mean a year or two waiting in limbo in the US.
Source: in the process for employment based green card and have a few friends who switched from TN/E3 visa to green card